Bruce says: Most likely The MAP (Manifold Absolute Pressure) sensor may not be receiving the correct vacuum signal, worn-down contacts on the ignition switch or a sticking IAC (Idle Air Control) valve are reasons why your Honda Odyssey may be stalling immediately after starting.
Take your car to AAMCO so they can perform a TranScan and Diagnostic Services, some locations may have a special for free diagnosis (usually $85), but you should check with the location first as they are independently owned and operated. You can find a location here